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Although intensively studied in recent years, the optimization of the transient (time-dependent) control of large real-world gas networks is still out of reach for current state-of-the-art approaches.
For this reason, we present further simplifications of the commonly used model, which lead to a linear description of the gas flow on pipelines.
In an empirical analysis of real-world data, we investigate the properties of the involved quantities and evaluate the errors made by our simplification.

A common approach to reduce the Euler equations' complexity for the simulation and optimization of gas networks is to neglect small terms that contribute little to the overall equations.
An example is the inertia term of the momentum equation since it is said to be of negligible size under real-world operating conditions.
However, this justification has always only been based on experience or single sets of artificial data points.
This study closes this gap by presenting a large-scale empirical evaluation of the absolute and relative size of the inertia term when operating a real-world gas network.
Our data consists of three years of fine-granular state data of one of the largest gas networks in Europe, featuring over 6,000 pipes with a total length of over 10,000 km.
We found that there are only 120 events in which a subnetwork consisting of multiple pipes has an inertia term of high significance for more than three minutes.
On average, such an event occurs less often than once every ten days.
Therefore, we conclude that the inertia term is indeed negligible for real-world transient gas network control problems.

In this paper, we describe an algorithmic framework for the optimal operation of transient gas transport networks consisting of a hierarchical MILP formulation together with a sequential linear programming inspired post-processing routine. Its implementation is part of the KOMPASS decision support system, which is currently used in an industrial setting.
Real-world gas transport networks are controlled by operating complex pipeline intersection areas, which comprise multiple compressor units, regulators, and valves. In the following, we introduce the concept of network stations to model them. Thereby, we represent the technical capabilities of a station by hand-tailored artificial arcs and add them to network. Furthermore, we choose from a predefined set of flow directions for each network station and time step, which determines where the gas enters and leaves the station. Additionally, we have to select a supported simple state, which consists of two subsets of artificial arcs: Arcs that must and arcs that cannot be used. The goal is to determine a stable control of the network satisfying all supplies and demands.
The pipeline intersections, that are represented by the network stations, were initially built centuries ago. Subsequently, due to updates, changes, and extensions, they evolved into highly complex and involved topologies. To extract their basic properties and to model them using computer-readable and optimizable descriptions took several years of effort.
To support the dispatchers in controlling the network, we need to compute a continuously updated list of recommended measures. Our motivation for the model presented here is to make fast decisions on important transient global control parameters, i.e., how to route the flow and where to compress the gas. Detailed continuous and discrete technical control measures realizing them, which take all hardware details into account, are determined in a subsequent step.
In this paper, we present computational results from the KOMPASS project using detailed real-world data.

This study examines the usability of a real-world, large-scale natural gas transport infrastructure for hydrogen transport. We investigate whether a converted network can transport the amounts of hydrogen necessary to satisfy current energy demands. After introducing an optimization model for the robust transient control of hydrogen networks, we conduct computational experiments based on real-world demand scenarios. Using a representative network, we demonstrate that replacing each turbo compressor unit by four parallel hydrogen compressors, each of them comprising multiple serial compression stages, and imposing stricter rules regarding the balancing of in- and outflow suffices to realize transport in a majority of scenarios. However, due to the reduced linepack there is an increased need for technical and non-technical measures leading to a more dynamic network control. Furthermore, the amount of energy needed for compression increases by 364% on average.

A common approach to reduce the Euler equations' complexity for the simulation and optimization of gas networks is to neglect small terms that contribute little to the overall equations.
An example is the inertia term of the momentum equation, which is said to be of negligible size under real-world operating conditions.
However, this justification has always only been based on experience or single sets of artificial data points.
This study closes this gap by presenting a large-scale empirical evaluation of the absolute and relative size of the inertia term when operating a real-world gas network.
Our data consists of three years of fine-granular state data of one of the largest gas networks in Europe, featuring over 6,000 pipes with a total length of over 10,000 km.
We found that there are only 120 events in which a subnetwork consisting of multiple pipes has an inertia term of high significance for more than three minutes.
On average, such an event occurs less often than once every ten days.
Therefore, we conclude that the inertia term is indeed negligible for real-world transient gas network control problems.

Optimizing the transient control of gas networks is a highly challenging task.
The corresponding model incorporates the combinatorial complexity of determining the settings for the many active elements as well as the non-linear and non-convex nature of the physical and technical principles of gas transport.
In this paper, we present the latest improvements of our ongoing work to solve this problem for real-world, large-scale problem instances:
By adjusting our mixed-integer non-linear programming model regarding the gas compression capabilities in the network, we reflect the technical limits of the underlying units more accurately while maintaining a similar overall model size.
In addition, we introduce a new algorithmic approach that is based on splitting the complexity of the problem by first finding assignments for discrete variables and then determining the continuous variables as locally optimal solution of the corresponding non-linear program.
For the first task, we design multiple different heuristics based on concepts for general time-expanded optimization problems that find solutions by solving a sequence of sub-problems defined on reduced time horizons.
To demonstrate the competitiveness of our approach, we test our algorithm on particularly challenging historic demand scenarios.
The results show that high-quality solutions are obtained reliably within short solving times, making the algorithm well-suited to be applied at the core of time-critical industrial applications.

Due to the current and foreseeable shifts in energy production, the trading and transport operations of gas will become more dynamic, volatile, and hence also less predictable.
Therefore, computer-aided support in terms of rapid simulation and control optimization will further broaden its importance for gas network dispatching.
In this paper, we aim to contribute and openly publish two new mathematical models for regulators, also referred to as control valves, which together with compressors make up the most complex and involved types of active elements in gas network infrastructures.
They provide full direct control over gas networks but are in turn controlled via target values, also known as set-point values, themselves.
Our models incorporate up to six dynamical target values to define desired transient states for the elements' local vicinity within the network.
That is, each pair of every two target values defines a bounding box for the inlet pressure, outlet pressure as well as the passing mass flow of gas.
In the proposed models, those target values are prioritized differently and are constantly in competition with each other, which can only be resolved dynamically at run-time of either a simulation or optimization process.
Besides careful derivation, we compare simulation and optimization results with predictions of the commercial simulation tool SIMONE.

Compressor stations are the heart of every high-pressure gas transport network.
Located at intersection areas of the network they are contained in huge complex plants, where they are in combination with valves and regulators responsible for routing and pushing the gas through the network.
Due to their complexity and lack of data compressor stations are usually dealt with in the scientific literature in a highly simplified and idealized manner.
As part of an ongoing project with one of Germany's largest Transmission System Operators to develop a decision support system for their dispatching center, we investigated how to automatize control of compressor stations. Each station has to be in a particular configuration, leading in combination with the other nearby elements to a discrete set of up to 2000 possible feasible operation modes in the intersection area.
Since the desired performance of the station changes over time, the configuration of the station has to adapt.
Our goal is to minimize the necessary changes in the overall operation modes and related elements over time, while fulfilling a preset performance envelope or demand scenario.
This article describes the chosen model and the implemented mixed integer programming based algorithms to tackle this challenge.
By presenting extensive computational results on real world data we demonstrate the performance of our approach.